Generic bi-Lyapunov stable homoclinic classes
Dynamical Systems
2015-05-13 v4
Abstract
We study, for generic diffeomorphisms, homoclinic classes which are Lyapunov stable both for backward and forward iterations. We prove they must admit a dominated splitting and show that under some hypothesis they must be the whole manifold. As a consequence of our results we also prove that in dimension 2 the class must be the whole manifold and in dimension 3, these classes must have nonempty interior. Many results on Lyapunov stable homoclinic classes for -generic diffeomorphisms are also deduced.
Cite
@article{arxiv.0903.4090,
title = {Generic bi-Lyapunov stable homoclinic classes},
author = {Rafael Potrie},
journal= {arXiv preprint arXiv:0903.4090},
year = {2015}
}
Comments
26 pages. This version includes an appendix that will not appear in the published version